#include #define rep(i,n) for(int i = 0; i < (int)(n); i++) #define ll long long #define fi first #define se second #define push_back pb #define show(x) cout << #x << " = " << x << "\n" using namespace std; typedef pair P; //f[j](x) = a[j]x + b[j]でaがjの増加に伴い単調減少する場合 template class CHT { private: using ptt = pair; bool check(ptt l1, ptt l2, ptt l3){ return (l2.first-l1.first)*(l3.second-l2.second)>=(l2.second-l1.second)*(l3.first-l2.first); } T f(int i, T x){ return lines[i].first * x + lines[i].second; } public: vector lines; CHT(){}; void add(T a, T b){ ptt line(a, b); while((int)lines.size() >= 2 && check(*(lines.end()-2), lines.back(), line)){ lines.pop_back(); } lines.emplace_back(line); } T get(T x){ static int head = 0; while((int)lines.size() - head >= 2 && f(head, x) > f(head + 1, x)){ head++; } return f(head, x); // int low = -1, high = lines.size() - 1; // while (high - low > 1) { // int mid = (high + low) / 2; // if(f(mid, x) >= f(mid+1, x)){ // low = mid; // }else{ // high = mid; // } // } // return f(high, x); } }; int main() { cin.tie(0); ios::sync_with_stdio(false); int n; cin >> n; vector a(n),x(n),y(n); rep(i,n){ cin >> a[i]; } rep(i,n){ cin >> x[i]; } rep(i,n){ cin >> y[i]; } CHT cht; cht.add(-2*x[0],x[0]*x[0]+y[0]*y[0]); rep(i,n){ if(i < n-1){ cht.add(-2*x[i+1],cht.get(a[i])+x[i+1]*x[i+1]+y[i+1]*y[i+1]+a[i]*a[i]); }else{ cout << cht.get(a[i])+a[i]*a[i] << "\n"; return 0; } } }